mgentry, power window switches handle the problem for you. The switch reverses the polarity depending on which direction the switch is pressed. There will be five or six leads on the back of the switch. Using a voltmeter, set it on the "ohms" setting and use the two voltmeter leads to touch two of the leads on the switch. Do this repeatedly until you have checked the continuity for all the wire lead combinations. This should be done in all three switch positions: left, middle, right.
What you are trying to find out is which wires are linked together in each switch position. Write it down and look at how the wire patterns change with each position. Two leads will be positive/negative input. It doesn't matter which is which. The other pair of leads will be for the window motor. You will be able to see in your drawing which wires are used in both up and down positions but the pattern changes. The wires for positive/negative input stay the same not matter the switch position.
Does that help or is it confusing?